Because of the complex terrain in the construction of longdistance buried pipeline, the elbows are widely used in pipeline systems. Due to its specificity in terms of shape and structure, elbows not only can change the axial direction of the pipeline, but also increase the flexibility of the pipeline. However, under the special conditions of environment, bends in the piping system are often the section of concentration of stress. In the certain conditions, plastic deformation occurs at the elbow, which poses a potential threat to the safe operation of pipelines. Through the application of software of finite element analysis, stress at a particular point (elbow) of buried pipeline were numerically calculated and analyzed. By numerical calculation and analysis, when the local pipeline under pressure in the radial direction, the distribution of values of Von Mises stress were obtained at the elbow, in the crossing segment of the buried pipeline. And when the length of the applied load, the bending angle and the radius of curvature of elbow were changed, the influence of the stress of the elbow was also obtained.